Extended SMART algorithms for non-negative matrix factorization invited paper

Andrzej Cichocki, Shun Ichi Amari, Rafal Zdunek, Raul Kompass, Gen Hori, Zhaohui He

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

80 Citations (Scopus)


In this paper we derive a family of new extended SMART (Simultaneous Multiplicative Algebraic Reconstruction Technique) algorithms for Non-negative Matrix Factorization (NMF). The proposed algorithms are characterized by improved efficiency and convergence rate and can be applied for various distributions of data and additive noise. Information theory and information geometry play key roles in the derivation of new algorithms. We discuss several loss functions used in information theory which allow us to obtain generalized forms of multiplicative NMF learning adaptive algorithms. We also provide flexible and relaxed forms of the NMF algorithms to increase convergence speed and impose an additional constraint of sparsity. The scope of these results is vast since discussed generalized divergence functions include a large number of useful loss functions such as the Amari α- divergence, Relative entropy, Bose-Einstein divergence, Jensen-Shannon divergence, J-divergence, Arithmetic-Geometric (AG) Taneja divergence, etc. We applied the developed algorithms successfully to Blind (or semi blind) Source Separation (BSS) where sources may be generally statistically dependent, however are subject to additional constraints such as non-negativity and sparsity. Moreover, we applied a novel multilayer NMF strategy which improves performance of the most proposed algorithms.

Original languageEnglish
Title of host publicationArtificial Intelligence and Soft Computing - ICAISC 2006 - 8th International Conference, Proceedings
PublisherSpringer Verlag
Number of pages15
ISBN (Print)3540357483, 9783540357483
Publication statusPublished - 2006
Externally publishedYes
Event8th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2006 - Zakopane, Poland
Duration: 25 Jun 200629 Jun 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4029 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2006


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